We theoretically demonstrate for the first time that a single free electron in circular/spiral motion emits twisted photons carrying well defined orbital angular momentum along the axis of the electron circulation, in adding to spin angular momentum. We show that, when the electron velocity is relativistic, the radiation field contains harmonic components and the photons of l-th harmonic carry  l total angular momentum for each. This work indicates that twisted photons are naturally emitted by free electrons and more ubiquitous in laboratories and in nature than ever been thought.

We theoretically show that a single free electron in circular motion radiates an electromagnetic wave possessing helical phase structure, which is closely related to orbital angular momentum carried by it. We experimentally demonstrate it by interference and double-slit diffraction experiments on radiation from relativistic electrons in spiral motion. Our results indicate that photons carrying orbital angular momentum should be created naturally by cyclotron/synchrotron radiations or Compton scatterings in various situations in cosmic space. We propose promising laboratory vortex photon sources in various wavelengths ranging from radio wave to gamma-rays.

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Quantum manipulation of populations and pathways in matter by light pulses, so-called coherent control, is currently one of the hottest research areas in optical physics and photochemistry. The forefront of coherent control research is moving rapidly into the regime of extreme ultraviolet wavelength and attosecond temporal resolution. This advance has been enabled by the development of high harmonic generation light sources driven by intense femtosecond laser pulses and by the advent of seeded free electron laser sources. Synchrotron radiation, which is usually illustrated as being of poor temporal coherence, hitherto has not been considered as a tool for coherent control. Here we show an approach based on synchrotron radiation to study coherent control in the extreme ultraviolet and attosecond regime. We demonstrate this capability by achieving wave-packet interferometry on Rydberg wave packets generated in helium atoms.